TSTP Solution File: SET065+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET065+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:33:49 EDT 2023
% Result : Theorem 0.15s 0.32s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 24 ~; 22 |; 17 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 37 (; 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X] :
( inductive(X)
<=> ( member(null_class,X)
& subclass(image(successor_relation,X),X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
? [X] :
( member(X,universal_class)
& inductive(X)
& ! [Y] :
( inductive(Y)
=> subclass(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ member(null_class,universal_class),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( ~ member(U,X)
| member(U,Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f47,plain,
! [X,Y] :
( ( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ? [U] :
( member(U,X)
& ~ member(U,Y) ) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
( ! [X,Y] :
( ~ subclass(X,Y)
| ! [U] :
( ~ member(U,X)
| member(U,Y) ) )
& ! [X,Y] :
( subclass(X,Y)
| ( member(sk0_0(Y,X),X)
& ~ member(sk0_0(Y,X),Y) ) ) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f53,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f130,plain,
! [X] :
( ( ~ inductive(X)
| ( member(null_class,X)
& subclass(image(successor_relation,X),X) ) )
& ( inductive(X)
| ~ member(null_class,X)
| ~ subclass(image(successor_relation,X),X) ) ),
inference(NNF_transformation,[status(esa)],[f29]) ).
fof(f131,plain,
( ! [X] :
( ~ inductive(X)
| ( member(null_class,X)
& subclass(image(successor_relation,X),X) ) )
& ! [X] :
( inductive(X)
| ~ member(null_class,X)
| ~ subclass(image(successor_relation,X),X) ) ),
inference(miniscoping,[status(esa)],[f130]) ).
fof(f132,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f135,plain,
? [X] :
( member(X,universal_class)
& inductive(X)
& ! [Y] :
( ~ inductive(Y)
| subclass(X,Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f136,plain,
( member(sk0_1,universal_class)
& inductive(sk0_1)
& ! [Y] :
( ~ inductive(Y)
| subclass(sk0_1,Y) ) ),
inference(skolemization,[status(esa)],[f135]) ).
fof(f138,plain,
inductive(sk0_1),
inference(cnf_transformation,[status(esa)],[f136]) ).
fof(f191,plain,
~ member(null_class,universal_class),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f202,plain,
member(null_class,sk0_1),
inference(resolution,[status(thm)],[f132,f138]) ).
fof(f203,plain,
! [X0] :
( ~ subclass(sk0_1,X0)
| member(null_class,X0) ),
inference(resolution,[status(thm)],[f202,f50]) ).
fof(f242,plain,
member(null_class,universal_class),
inference(resolution,[status(thm)],[f203,f53]) ).
fof(f243,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f242,f191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET065+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:20:45 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.15/0.32 % Refutation found
% 0.15/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.53 % Elapsed time: 0.014787 seconds
% 0.15/0.53 % CPU time: 0.013665 seconds
% 0.15/0.53 % Memory used: 3.810 MB
%------------------------------------------------------------------------------